NEW YORK -LRB- CNN -RRB- -- David Letterman told his audience Thursday that he is the victim of an alleged extortion attempt and admitted to having sexual relations with several members of his staff , according to a press release from his production company .

David Letterman admitted to having sexual relationships with female staff members , his company says .

Letterman made the announcement during taping of the `` Late Show . ''

`` This morning , I did something I 've never done in my life , '' Letterman told his audience , according to a release from Worldwide Pants Inc. `` I had to go downtown and testify before a grand jury . ''

The 62-year-old funnyman said he received a package three weeks ago from a person who claimed to have information about Letterman 's sexual dalliances , ultimately demanding $ 2 million to prevent public revelation .

Letterman said he went to the Manhattan District Attorney 's office , which conducted an investigation , and an arrest was made earlier Thursday .

In his grand jury testimony , Letterman said , he revealed the relations with members of his staff .

`` My response to that is , yes I have , '' he said . `` Would it be embarrassing if it were made public ? Perhaps it would . I feel like I need to protect these people -- I need to certainly protect my family . ''

It is not known when the sexual encounters with staffers took place .

Letterman married long-time partner Regina Lasko in March . The couple , who have been together since 1986 , have a son , Harry , 6 .

Letterman has been host of `` Late Show with David Letterman '' on CBS since 1993 after leaving NBC , where he was host of `` Late Night with David Letterman '' for 11 years . `` Late Show '' airs at 11:30 p.m. `` Late Night '' aired an hour later .

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Letterman tells audience he is the victim of an extortion attempt

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Host says someone threatened to reveal sexual relations unless he paid $ 2 million

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Host admitted having sexual relations with staff members in grand jury testimony

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Letterman makes revelation during his show 's taping on Thursday